In the computation of metal flux in aquatic systems, at consuming surfaces like organism membranes, diffusion processes of metal ions, ligands, and complex species, as well as the kinetic and thermodynamic aspects of their chemical interactions, must be considered. The properties of many natural ligands, however, are complicated (formation of successive complexes for simple ligands, polyelectrolytic properties and chemical heterogeneity for macromolecular ligands, large size distribution and fractal structure for suspended aggregates). These properties should be properly modeled to get the correct values of the chemical rate constants and diffusion coefficients required for flux computations. The selection of the most appropriate models and parameter values is far from straightforward. This series of papers discusses the various models and compiles the parameters needed for the three most important types of complexants found in aquatic systems: the small, simple ligands, the fulvic and humic compounds, and the colloidal "particles" or aggregates. In particular, new approaches are presented to compute the rate constants of metal complex formation, with both fulvics/humics and particles/aggregates. The method to include the site distribution of fulvics/humics and the size distribution of particles/aggregates in metal flux computation at consuming interfaces is also discussed in detail. These models and parameters are discussed critically and presented in the same framework, forthe computation of metal flux in presence of any of the above complexants or mixtures. Such parameters, largely spread in the literature, are gathered here and selected specifically for environmental applications. The focus in Part I of the series is on simple ligands and fulvic/humic compounds. Part II deals with particulate and aggregate complexants.
In complicated environmental or biological systems, the fluxes of chemical species at a consuming interface, like an organism or an analytical sensor, involve many coupled chemical and diffusion processes. Computation of such fluxes thus becomes difficult. The present paper describes an approximate approach, based on the so-called reaction layer concept, which enables one to obtain a simple analytical solution for the steady-state flux of a metal ion at a consuming interface, in the presence of many ligands, which are in excess with respect to the test metal ion. This model can be used for an unlimited number of ligands and complexes, without limit for the values of the association/dissociation rate constants or diffusion coefficients. This approximate solution is compared with a rigorous approach for the computation of the fluxes based on an extension of a previously published method (J. Galceran, J. Puy, J. Salvador, J. Cecília, F. Mas and J. L. Garcés, Phys. Chem. Chem. Phys., 2003, 5, 5091-5100). The comparison is performed for a very wide range of the key parameters: rate constants and diffusion coefficients, equilibrium constants and ligand concentrations. Their combined influence is studied in the whole domain of fully labile to non-labile complexes, via two combination parameters: the lability index, L, and the reaction layer thickness, mu. The results show that the approximate solution provides accurate results in most cases. However, for particular combinations of metal complexes with specific values of L or mu, significant differences between the approximate and rigorous solutions may occur. They are evaluated and discussed. These results are important for three reasons: (i) they enable the use of the approximate solution in a fully reliable manner, (ii) when present, the differences between approximate and rigorous solution are largely due to the coupling of chemical reactions, whose importance can thus be estimated, (iii) due to its simple mathematical expression, the individual contribution of each metal species to the overall flux can be computed.
Environmental context. Until now there was no user-friendly code for metal flux computations in natural mixtures of aquatic complexants, which are however essential for prediction of metal bioavailability. The present paper describes the capabilities and limitations of one of the only two such codes presently available, called FLUXY. The results of FLUXY are compared with those of another code, and it is shown that it enables quick computation and is applicable to natural ligands under many environmental conditions. Abstract. The computation of metal fluxes at consuming interfaces like microorganisms or bioanalogical sensors is of great importance in ecotoxicology. The present paper describes the application of a simple code, FLUXY, for the computation of steady-state metal fluxes in the presence of a very large number of complexes, with broadly varying values of equilibrium constants, rate constants and diffusion coefficients. This code includes two major limiting assumptions, namely, (i) the existence of excess of ligand (L) compared with metal (M), and (ii) the fact that in a series of successive MLn complexes, the reaction is the rate-limiting step in flux computation. The domains of rate constants for which these assumptions are valid are tested systematically, and the corresponding errors are evaluated by comparison with the exact results given by another code: MHEDYN. FLUXY is then applied and compared with MHEDYN for case studies typical of aquatic systems, namely (i) a culture medium containing simple ligands; (ii) solutions of fulvic compounds including a broad distribution of complex stability and rate constants; and (iii) suspensions of aggregates with a broad size distribution. It is shown that FLUXY gives good results for cases (i) and (iii). Application to case (ii) (fulvic compounds) is also feasible under conditions that are clearly described. Altogether, FLUXY and MHEDYN are complementary. In particular, FLUXY only computes steady-state fluxes and requires the fulfilment of a few conditions, but when these are met, computations require much less computer time than MHEDYN.
The present study examines the interaction of amine-and carboxyl-PEG core/shell quantum dots (QDs) with metal resistant bacterium Cupriavidus metallidurans CH34. The evolution of the number of QDs, their hydrodynamic radius, diffusion coefficients, and single particle fluorescence were characterized before and during the contact with bacterium by fluorescence correlation spectroscopy (FCS). The obtained results showed that at nanomolar concentrations the amine-and carboxyl-PEG-QDs with average hydrodynamic radiuses of 16.4 and 13.5 nm, form stable dispersions in the absence and presence of 15 mgC L -1 HA. The decrease of the number of fluorescent particles in the bacterial medium, determined by FCS, together with the increase of the fluorescence of bacterial cells over the background, found by flow cytometry (FCM), demonstrated the association of QDs to C. metallidurans. Furthermore, QDs enhanced the level of the reactive oxygen species in the bacterial cells and augmented the percentage of the cells with damaged and leaky membranes as probed by FCM in combination with 5-(and-6)-carboxy-2′7′-dichlorodihydrofluorescein diacetate and propidium iodide stains. No difference in the behavior of amine-and carboxyl-PEG-QDs was found, suggesting that different functional groups in the surface coating have no effect on bacterium-QD interactions under the studied conditions. The presence of HA does not affect the hydrodynamic characteristics of the functionalized QDs, but prevented the damage to the bacterial membrane. The slight decrease in the bacterial growth found after exposure of C. metallidurans to these QDs was attributed to the nanoparticles themselves rather the cadmium, zinc, or selenium ions released from the QDs.
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